The word inauguration originally referred not to the ceremonial transfer of power but to the act of divination that preceded it.
It makes sense that the state, before embarking on a major endeavor such as a war or a change of government, should consult the will of the gods on the matter. The augurs (diviners) take the auguries (omens) to see what the future will bring.
I haven't heard yet what omens the US College of Augurs got today. (Their headquarters is down on the Mall someplace, I think; I'm pretty sure I walked past it a few years ago.) No doubt tomorrow it will be all over the web.
(State augur. Now there's a job I wouldn't mind having. I hear the benefits are great.)